Quantile Function of the 4-Parameter Asymmetric Exponential Power Distribution

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Description

This function computes the quantiles of the 4-parameter Asymmetric Exponential Power distribution given parameters (ξ, α, κ, and h) of the distribution computed by paraep4. The quantile function of the distribution given the cumulative distribution function F(x) is
For F < F(ξ),

x(F) = ξ - ακ[γ^{(-1)}((1+κ^2)F/κ^2,\; 1/h)]^{1/h}\mbox{,}

and for F ≥ F(ξ),

x(F) = ξ + \frac{α}{κ}[γ^{(-1)}((1+κ^2)(1-F),\; 1/h)]^{1/h} \mbox{,}

where x(F) is the quantile x for nonexceedance probability F,
ξ is a location parameter, α is a scale parameter,
κ is a shape parameter, h is another shape parameter, γ^{(-1)}(Z, shape) is the inverse of the upper tail of the incomplete gamma function. The range of the distribution is -∞ < x < ∞. The inverse upper tail of the incomplete gamma function is qgamma(Z, shape, lower.tail=FALSE) in R. The mathematical definition of the upper tail of the incomplete gamma function shown in documentation for cdfaep4.

Usage

Arguments

f

Nonexceedance probability (0 ≤ F ≤ 1).

para

The parameters from paraep4 or similar.

paracheck

A logical controlling whether the parameters are checked for validity. Overriding of this check might be extremely important and needed for use of the quantile function in the context of TL-moments with nonzero trimming.